The New York Giants succeeded Saturday in reducing the NFC East race to a winner-take-all game next weekend at the Meadowlands between them and the Dallas Cowboys.

The Giants stayed in the running for the division title by beating the Jets, 29-14, at MetLife Stadium in New York’s NFL version of a city title game Saturday afternoon, with major playoff implications for both teams. The Jets fell behind the Cincinnati Bengals in the chase for the second of the AFC’s two wild-card playoff spots.

“This is a big win because of everything that was on the line . . . and we knew we had to win this game to have a shot to keep ourselves in the playoff hunt,” Giants quarterback Eli Manning said at a postgame news conference. “Playing against the crosstown rivals — a lot on the line. Guys stepped up and made some big plays. It wasn’t the prettiest game offensively that we’ve ever played, but we didn’t make many mistakes.”

The New England Patriots clinched a first-round bye in the AFC playoffs as NFL teams spent the day jockeying for postseason spots and seeds on the next-to-last weekend of the regular season.

The Baltimore Ravens and Pittsburgh Steelers both won Saturday and remained tied atop the AFC North at 11-4. The Ravens have a tiebreaker edge after beating the Steelers twice this season, and can clinch the division with a victory over the Bengals next week.

The Detroit Lions secured their first playoff berth since the 1999 season. The San Francisco 49ers moved a step closer to a first-round bye in the NFC with their triumph over the Seattle Seahawks. A loss Monday night by the New Orleans Saints would give the 49ers a bye.

The day’s most eagerly anticipated game came between the New York area’s two teams. Both were coming off lopsided losses, and there was plenty of verbal sparring between the teams during the week. Another issure arose Saturday: It was a Jets home game, and the Super Bowl logos outside the Giants’ locker room were covered by curtains.

But it was the Giants who emerged with local bragging rights and moved a step closer to the playoffs.

“It will be a very nice Christmas Eve and Christmas for the guys, starting tonight,” Giants Coach Tom Coughlin said at his news conference following the game.

The Giants improved their record to 8-7, tied with the Cowboys atop the NFC East. The Cowboys lost in Arlington, Tex., to the Philadelphia Eagles, 20-7. The game at Cowboys Stadium was rendered meaningless for playoff purposes once the Giants won earlier in the day.

Even if Dallas had won Saturday, the Cowboys-Giants game next Sunday would have been for the NFC East crown. The Giants hold a tiebreaker edge over the Cowboys after beating them in the teams’ first meeting of the season. Cowboys quarterback Tony Romo left Saturday’s game after hurting his throwing hand on his team’s opening offensive series. X-rays reportedly showed no fracture and Romo’s injury was described as a bruise. The Eagles were eliminated from playoff contention, thanks to the Giants’ triumph, even with their victory over the Cowboys.

Coughlin hurt his leg during the game when he absorbed a hit while standing on the sideline, but said afterward that he’d never felt better.

“Nobody is worried about how fast I am,” Coughlin said. “And nobody was ever worried about that, as a matter of fact. I got it on the knee but I think it is up higher. You can imagine what the players said when they went by: ‘No toughness, no championship.’ I said, ‘You are exactly right.’ ”

The Patriots are ensured of having the first playoff weekend off after overcoming a 17-0 deficit to beat the Miami Dolphins, 27-24.

“It wasn’t our best effort of the season,” Patriots Coach Bill Belichick said at his postgame news conference. “But we’ve got to give the players a lot of credit for coming back in the second half down 17-0. They played a good enough half of football — happy to win. . . . It’s a good way to go into the little Christmas break here for a couple days — recharge, come back and hopefully be able to finish strong.”

The Lions had been tied with the Buffalo Bills for the NFL’s longest playoff drought. But they ended that, securing an NFC wild-card spot with a 38-10 triumph over the San Diego Chargers.

The Denver Broncos fell into a first-place tie in the AFC West with the Oakland Raiders with identical 8-7 records. Quarterback Tim Tebow threw four interceptions, two of which were returned for touchdowns, as the Broncos lost to the Bills, 40-14. But the Broncos still can win the division with a victory over the Kansas City Chiefs next weekend in the regular season finale.

“Everything’s still on the table,” Tebow said at his postgame news conference. “Then we have to go and execute and play a little better. Hopefully we can get in the tournament.”

The Green Bay Packers can secure the top seed in the NFC playoffs with a win Sunday night over the Chicago Bears. The Saints can clinch the NFC South if they beat the Atlanta Falcons on Monday night. The Falcons get the other wild-card spot in the NFC with a win Monday or a loss Sunday by the Bears.